Problem: Solve for $x$ and $y$ using elimination. ${-x+6y = 54}$ ${x-5y = -44}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-x+6y = 54}\thinspace$ to find $x$ ${-x + 6}{(10)}{= 54}$ $-x+60 = 54$ $-x+60{-60} = 54{-60}$ $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ You can also plug ${y = 10}$ into $\thinspace {x-5y = -44}\thinspace$ and get the same answer for $x$ : ${x - 5}{(10)}{= -44}$ ${x = 6}$